Method for determining a preferential minimum power set point, method for controlling a plurality of water heaters and associated device

ABSTRACT

A method for determining a preferential minimum power set point by a consumer i, said consumer including an electric water heater, the method including determining the state of the consumer i at an instant k; determining a minimum power set point P c   min (i,k) at the instant k as a function of the state of the consumer i determined during the determining of the state of the consumer i at an instant k; determining a minimum power set point P c   min (i,k+1:K) at the instants k+1 to K as a function of the predicted state of the consumer i estimated from the state of the consumer i determined during the determining of the state of the consumer i at an instant k; determining a preferential minimum power set point P c   min_pref (i,k) as a function of the minimum power set point P c   min (i,k) at the instant k and of the minimum power set point P c   min (i,k+1:K) at the instants k+1 to K.

TECHNICAL FIELD OF THE INVENTION

The technical field of the invention is that of driving of hot water consumption for the purpose of maximising renewable energy self-consumption. More particularly, the invention relates to a method for determining a preferential minimum power set point as well as a method for driving a plurality of water heaters on a network including a plurality of consumers i. It also relates to a device implementing such methods.

TECHNOLOGICAL BACKGROUND OF THE INVENTION

In the context of renewable energy production, for example using a photovoltaic panel, it is known to individually drive each facility so as to satisfy each consumer's demand while maximising the consumption of locally produced energy. However, it may be advantageous to manage production, no longer individually, but collectively by distributing locally produced energy between different consumers depending on needs. To do so, it is possible to complete the facility with batteries or any other storage form so as to maximise the use of the locally produced energy. However, in order to limit battery use, it is also possible to use electric equipment for hot water production by considering the latter either to an electric charge which will therefore consume energy, or to a heat storage means (or thermal storage means) which will therefore store energy. Such a system can therefore be driven using two set points: activation or deactivation of the electrical consumption related to water heating or a temperature set point of hot water.

Generally, the electric water heaters can have several compartments or several resistors positioned at different heights of the water heater, so as to bring modularity in water heating and to provide the possibility of driving consumption and temperature for different water volumes. When seeking to optimise hot water production and consumption, it is necessary to take production or consumption predictions as well as information relating to the state of each consumer (number of occupants associated with the consumer, past hot water consumption, etc.) into account. Moreover, it is necessary to take account of the notion of need and comfort.

For this, modern smart meters, such as the Linky meter, enable the electric consumption to be communicated in real time for smartly driving electric facilities. For example, document FR 3 033 394 A1 shows a water heater management system with a dedicated photovoltaic facility which enables energy produced by photovoltaic panels in thermal form to be absorbed in the water heater(s) of the facility. The system further uses weather forecasts so as to determine whether the water heater has to use energy provided by the photovoltaic panels (daytime charging) or on the contrary use energy of the network to which the system is connected (night time charging). Similarly, the system is shown in “Using Electric Water Heaters (EWHs) for Power Balancing and Frequency Control in PV-Diesel Hybrid Mini-GridsK”; Elamari et al, World Energy Renewable Congress 2011, Sweden which describes a strategy for managing water heaters within the scope of frequency management in a micro-network.

Generally, driving a facility can be made in two different ways. The first one is based on a balanced distribution. Its advantage is to only necessitate few data, but it does not allow an optimum driving, that is a driving maximising consumption of the locally produced energy. The second one is based on an optimum distribution calculated using mathematical methods from operational research requiring electric consumption predictions of the different consumers as well as the local production prediction. It is therefore based on predictions consisting of long data series throughout a production/consumption period (typically one day) which often have a significant error level resulting either in the consumer's dissatisfaction in terms of comfort and/or need, or in a sub-optimum driving.

There is therefore a need for a method enabling an optimum driving to be achieved without resorting to complex data series.

SUMMARY OF THE INVENTION

The invention offers a solution to the problems previously discussed, by providing a driving method not requiring production predictions, but generating set points based on data relating to the ongoing production period.

For this, a first aspect of the invention relates to a method for determining a preferential minimum power set point by a consumer i, said consumer comprising an electric water heater, said method comprising:

-   -   a step of determining the state of the consumer i at an instant         k;     -   a step of determining a minimum power set point P_(c)         ^(min)(i,k) at the instant k as a function of the state of the         consumer i determined during the step of determining the state         of the consumer i at an instant k;     -   a step of determining a minimum power set point P_(c)         ^(min)(i,k+1:K) at the instants k+1 to k as a function of the         predicted state of the consumer i estimated from the state of         the consumer i determined during step of determining the state         of the consumer i at an instant k;     -   a step of determining a preferential minimum power set point         P_(c) ^(min_pref)(i,k) as a function of the minimum power set         point P_(c) ^(min)(i,k) at the instant k and of the minimum         power set point P_(c) ^(min)(i,k+1:K) at the instants k+1 to k.

Thus, no production prediction is necessary for determining a driving set point, this determination being performed based on data relating to the ongoing production period.

In one embodiment, the step of determining the state of the consumer i at the instant k comprises:

-   -   a sub-step of acquiring the power P(i,k) consumed by the water         heater of the consumer i at the instant k;     -   a sub-step of determining the number of persons Per(i,k) at the         instant k associated with said consumer i.

In one embodiment, the step of determining the minimum power set point P_(c) ^(min)(i,k) at the instant k comprises:

-   -   a sub-step of determining the minimum necessary amount of hot         water Eau_(min)(i,1:k) at the instant k as a function of the         number of persons Per(i,k) associated with the consumer i;     -   a sub-step of determining a minimum power set point P_(c)         ^(min)(i,k) at the instant k as a function of the necessary         amount of hot water Eau_(min)(i,1:k) at the instant k determined         in the previous sub-step.

In one embodiment, the step of determining the minimum power set point P_(c) ^(min)(i,k+1:K) at the instants k to K comprises:

-   -   a sub-step of determining a predicted amount of hot water         Eau^(prev)(i,k+1:K) consumed at the instants k+1 to K as a         function of a number of persons associated with said consumer i         Per⁺¹(i,k+1,K) in which Per⁺¹(i,k)=min(Per(i,k)+1,N_(i)) with         N_(i) being the maximum number of persons associated with said         consumer i;     -   a sub-step of determining the minimum power set point P_(c)         ^(min_pref)(i,k) at the instants k+1 to K as a function of the         predicted amount of hot water Eau^(prev)(i,k+1:K) determined         during the previous sub-step.

A second aspect of the invention relates to a method for driving a plurality of water heaters on a network including a plurality of consumers i, each consumer i from the plurality of consumers i comprising a water heater from the plurality of water heaters, said method comprising:

-   -   a step of receiving, for each consumer i from the plurality of         consumers i, a preferential minimum power set point P_(c)         ^(min_pref)(i,k);     -   for each consumer i from the plurality of consumers i, a step of         determining a power set point P_(c)(i,k) at the instant k as a         function of the preferential minimum power set point P_(c)         ^(min_pref)(i,k).

In one embodiment, the method according to a second aspect of the invention comprises, before the receiving step, for each consumer i from the plurality of consumers i, a step of implementing a method according to a first aspect of the invention so as to obtain, for each consumer i, a preferential minimum power set point P_(c) ^(min_pref)(i,k).

In one embodiment, the step of determining a power set point P_(c)(i,k) at the instant k comprises:

-   -   a sub-step of determining the optimum electric modulation at the         instant k;     -   a sub-step of determining an optimum power set point P_(c)         ^(opt)(i,k) corresponding to the modulation distribution among         each consumer i, said distribution being performed in proportion         to the preferential minimum set points P_(c) ^(min_pref)(i,k);     -   a sub-step of determining the power set point P_(c)(i,k), said         power set point P_(c)(i,k) at the instant k being equal to the         maximum among the optimum power set point P_(c) ^(opt)(i,k) and         the preferential minimum set point P_(c) ^(min_pref)(i,k).

In one embodiment, the step of determining a power set point P_(c)(i,k) at the instant k comprises:

-   -   a sub-step of determining the optimum electric modulation at the         instant k;     -   a sub-step of determining an optimum power set point P_(c)         ^(opt)(i,k) corresponding to the maximisation of the following         relationship:

Σs(i,k)×n(i,k)

-   -   where S(i,k) is the satisfaction of consumer i at the instant k         with S=1 when the satisfaction is maximum and S=0 when the         satisfaction is minimum and n(i,k) the efficacy of power use         determined using the following formula:

${n\left( {i,k} \right)} = \left\{ \begin{matrix} {{\frac{P_{c}^{opt}\left( {i,k} \right)}{P\left( {i,k} \right)}{si}\mspace{14mu} {P\left( {i,k} \right)}} > 0} \\ {{0\mspace{14mu} {si}\mspace{14mu} {P\left( {i,k} \right)}} = 0} \end{matrix} \right.$

-   -   a sub-step of determining the power set point P_(c)(i,k), said         power set point P_(c)(i,k) at the instant k being equal to the         maximum among the optimum power set point P_(c) ^(opt)(i,k) and         the preferential minimum set point P_(c) ^(min_pref)(i,k).

A third aspect of the invention relates to a device comprising means for implementing a method according to a first or a second aspect of the invention.

A fourth aspect of the invention relates to a computer program comprising instructions which cause the device according to a third aspect of the invention to carry out the steps of the method according to a first or a second aspect of the invention.

A fifth aspect of the invention relates to a computer readable medium, on which the computer program according to a fourth aspect of the invention is recorded.

The invention and its different applications will be better understood upon reading the following description and upon examining the accompanying figures.

BRIEF DESCRIPTION OF THE FIGURES

The figures are shown by way of indicating and in no way limiting purposes for the invention.

FIG. 1 shows a flowchart of a method according to a first aspect of the invention.

FIG. 2 shows a flowchart of a method according to a second aspect of the invention.

DETAILED DESCRIPTION

Unless otherwise indicated, a same element appearing on different figures has a single reference.

In the following, the notation hereinafter detailed will be used.

Each consumer is associated with an index i, said index being such that i∈[1,I] with I being the total number of consumers.

Each time range of the production/consumption period is associated with an index k, said index being such that k∈[1,K], with K being the total number of time ranges during the production/consumption period. Moreover, each time range has a time duration Δ so that K×Δ is equal to the duration of the production/consumption period. In the following, the term “instant k” will be used to refer to the time range k. For example, A can be equal to one minute and K equal to 1440, which corresponds to a 24 h production period. The instant k should be understood as the instant during which the state of the consumer is determined and during which the set point is established using a method according to the invention.

The power consumed by the water heater of the consumer i at the instant k is noted P(i,k). Moreover, the power consumed by the water heater of the consumer i between the instants k₁ and k₂ is noted P(i,k₁:k₂) and corresponds to a vector the coordinates of which are the power consumed by the water heater of the consumer i during the instants k₁ to k₂. For example, the vector P(i,1:3) is equivalent to the vector (P(i,1),P(i,2),P(i,3)).

The water heater temperature of the consumer i at the instant k is noted T(i,k). Moreover, the water heater temperature of the consumer i between the instants k₁ and k₂ is noted T(i,k₁:k₂) (once again, this is a vector).

The set point power given to the water heater of the consumer i at the instant k is noted P_(c)(i,k). Moreover, the set point power given to the water heater of the consumer i between the instants k₁ and k₂ is noted P_(c) ^(min)(i,k₁:k₂) (once again, this is a vector).

The number of persons associated with a consumer i at the instant k is noted Per(i,k). This number of persons is always such that 0≤Per(i,k)≤N_(i), with N_(i) being the maximum number of persons associated with the consumer i. Moreover, the number of persons associated with the consumer i between the instants k₁ and k₂ is noted Per(i,k₁:k₂)(once again, this is a vector).

The amount of hot water consumed by the consumer i during the time range k is noted Eau(i,k). Moreover, the amount of hot water consumed by the consumer i between the instants k₁ and k₂ is noted Eau(i,k₁:k₂) (once again, this is a vector).

The minimum necessary amount of hot water for the consumer i at the instant k is noted Eau_(min)(i,k).

The total amount of water in the hot water tank when the latter is full, of the consumer i is noted V_(total)(i).

The cold water temperature at the input of the hot water tank of the consumer i at the instant k is noted T_(eaufroide)(i,k).

The conversion factor of electric power into thermal power relative to the water heater of the consumer i is noted R(i).

The room temperature of the hot water tank premises associated with the consumer i at the instant k is noted T_(amb)(i,k).

The thermal dispersion coefficient between the tank and the room temperature associated with the consumer i is noted Loss_(facteur)(i).

A first aspect of the invention illustrated in FIG. 1 relates to a method 100 for determining a preferential minimum power set point by a consumer i, said consumer comprising an electric water heater. Hot water from the water heater can in particular be used for sanitary facilities, for the air conditioning and/or heating. The method therefore aims at determining (possibly to provide it to a management system) a set point value to be fulfilled for a proper management of the water heater of a given consumer i.

For this, the method 100 according to a first aspect of the invention includes, a step 1E1 of determining the state of the consumer i at the instant k. The state of a consumer may include the power consumed by the water heater P(i,k). It may also include the number of persons Per(i,k) associated with the consumer i at the instant k. Indeed, each consumer i may correspond to a household or more generally to a building, that is to one or more persons. Of course, the power consumed by the water heater P(i,k) of the consumer i will therefore depend on the number of persons Per(i,k) present at each instant k.

In one embodiment, the step 1E1 of determining the state of the consumer i at the instant k comprises a sub-step 1E11 of acquiring the power P(i,k) consumed by the water heater of the consumer i at the instant k. This acquisition can be for example performed using a smart meter. At the end of this sub-step 1E11, the power P(i,k) consumed by the water heater of the consumer i at the instant k is known.

In one embodiment, the step 1E1 of determining the state of the consumer i also comprises a sub-step 1E12 of determining the number of persons Per(i,k) at the instant k associated with the consumer i. The number of persons associated with the consumer i can be for example determined by measuring the CO₂ amount. This number can also be determined from geolocation data obtained using a smart phone (or computerphone). Other information may also be used, for example working hours in the case of a company or a combination of said information. At the end of this sub-step 1E12, the number of persons Per(i,k) associated with the consumer i at the instant k is known.

At the end of the step 1E1 of determining the state of the consumer i at the instant k, the number of persons Per(i,k) as well as the power consumed P(i,k) by the water heater at the instant k associated with said consumer i, are known.

Once the state of the consumer i is known, it is possible to assess the needs of the consumer i at the instant k and to determine a minimum power set point P_(c) ^(min)(i,k) for the water heater of the consumer i at the instant k. For this, the method 100 further includes, a step 1E2 of determining a minimum power set point P_(c) ^(min)(i,k) at the instant k as a function of the state of the consumer i determined during the step 1E1 of determining the state of the consumer i at an instant k.

In one embodiment, the step 1E2 of determining the minimum power set point P_(c) ^(min)(i,k) at the instant k comprises a sub-step 1E21 of determining the minimum necessary amount of hot water Eau_(min)(i,k) at the instant k as a function of the number of persons Per(i,k) associated with the consumer i. In one embodiment, the amount of hot water Eau_(min)(i,k) associated with the consumer i is determined by taking preferences of each person present into account.

The step 1E2 of determining a minimum power set point P_(c) ^(min)(i,k) at the instant k also comprises a sub-step 1E22 of determining a minimum power set point P_(c) ^(min)(i,k) at the instant k as a function of the minimum necessary amount of hot water Eau_(min)(i,k) at the instant k determined in the previous sub-step 1E21.

In one embodiment, the minimum power set point P_(c) ^(min)(i,k) at the instant k is given by the following formula:

${P_{c}^{\min}\left( {i,k} \right)} = \frac{\frac{T_{eau}\left( {i,k} \right)}{\Delta} + {\left( {{r_{eau}\left( {i,{k - 1}} \right)} - {T_{amb}\left( {i,k} \right)}} \right) \times {{Loss}_{facteur}(i)}} - \frac{\begin{matrix} {{{T_{eau}\left( {i,{k - 1}} \right)} \times \left( {{V_{total}(i)} - {{Eau}_{\min}\left( {i,k} \right)}} \right)} +} \\ {{T_{saufroide}\left( {i,k} \right)} \times {{Eau}_{\min}\left( {i,k} \right)}} \end{matrix}}{V_{total}(i)}}{R(i)}$

The conversion factor of electric power into thermal power R(i) and/or the thermal dispersion coefficient between the tank and room temperature Loss_(facteur)(i) can be determined from measurements and/or provided by the water heater manufacturer.

In one embodiment, when the cold water temperature at the input of the tank T_(eaufroide)(i,k) is not known (for example, no sensor is present), the value of this temperature can be chosen as being equal to a predetermined value, for example 15° C. in summer and 12° C. in winter.

In one embodiment, when the room temperature T_(amb)(i,k) of the hot water tank premises associated with the consumer i is not known (for example, no sensor is present), the value of this temperature can be chosen as being equal to a predetermined value, for example equal to 22° C.

The method 100 subsequently includes, a step 1E3 of determining a minimum power set point P_(c) ^(min)(i,k+1:K) at the instants k+1 to K.

In one embodiment, the step 1E3 of determining a minimum power set point P_(c) ^(min)(i,k+1:K) at the instants k+1 to K comprises a sub-step 1E31 of determining the predicted amount of hot water Eau^(prev)(i,k+1:K) consumed at the instants k+1 to K as a function of the number of persons associated with said consumer plus one person (that is Per(i,k)+1 if Per(i,k)+<N_(i) or N_(i) otherwise) at the instants k+1 to K, noted Per⁺¹(i,k+1:K) in the following. In other words, the aim is to determine the necessary amount of hot water by hypothesizing that the number of persons associated with the consumer i at an instant k is equal to Per⁺¹(i,k)=min (Per(i,k)+1,N_(i)).

In one embodiment, the hot water temperature T(i,k) is also taken into account during the sub-step of determining the predicted amount of hot water Eau^(prev)(i,k+1:K) at the instants k+1 to K.

In one embodiment, the coefficients of the predicted amount of hot water Eau^(prev)(i,k+1:K) can be determined using the following formula:

${{Eau}^{prev}\left( {i,k^{\prime}} \right)} = \frac{{{{Eau}_{moy}(i)} \times {{Per}^{+ 1}\left( {i,k} \right)}} - {\sum_{k^{''} = 1}^{k^{\prime}}{{Eau}\left( {i,k^{''}} \right)}}}{\left( {K - k^{\prime}} \right) \times \Delta {\forall{k^{\prime} \in \left\lbrack {{k + 1},K} \right\rbrack}}}$

Where Eau_(moy)(i) is the average water amount consumed by the consumer i over a given period, for example the production period (for example determined from data from the previous production periods).

For example, Eau^(prev)(i,3:5)=[Eau^(prev)(i,3),Eau^(prev)(i,4),Eau^(prev)(i,5)]. In one embodiment, the sub-step 1E31 of determining the predicted amount of hot water Eau^(prev)(i,k+1:K) consumed at the instants k+1 to K comprises a phase of determining an arrival time of the additional person, the predicted amount of hot water Eau^(prev)(i,k+1:K) being then determined as the function of said arrival time. The predicted arrival time can be determined by a learning method, as a function of previously recorded actual arrival times. Alternatively or additionally, the predicted arrival time can be determined as a function of working hours or any other information regarding schedule of the person(s) associated with consumer i considered. Alternatively or additionally, the predicted arrival time can be determined using geolocation information regarding the persons associated with the consumer considered.

In one embodiment, the step 1E3 of determining a minimum power set point P_(c) ^(min)(i,k+1:K) at the instants to k+1 to K also comprises a sub-step 1E32 of determining the minimum power set point P_(c) ^(min)(i,k+1:K) at the instants k+1 to K as a function of the predicted amount of hot water Eau^(prev)(i,k+1:K) consumed at the instants k+1 to K determined during the previous sub-step 1E31.

In one embodiment, the coefficients of the minimum power set point P_(c) ^(min)(i,k+1:K) at the instants k+1 to K can be calculated using the following formula:

${P_{c}^{\min}\left( {i,k^{\prime}} \right)} = {\frac{\frac{T_{eau}\left( {i,k^{\prime}} \right)}{\Delta} + {\left( {{T_{eau}\left( {i,{k^{\prime} - 1}} \right)} - {T_{amb}\left( {i,k^{\prime}} \right)}} \right) \times {{Loss}_{facteur}(i)}} - \frac{\begin{matrix} {{{T_{eau}\left( {i,{k^{\prime} - 1}} \right)} \times \left( {{V_{total}(i)} - {{Eau}^{prev}\left( {i,k^{\prime}} \right)}} \right)} +} \\ {{T_{saufroide}\left( {i,k^{\prime}} \right)} \times {{Eau}^{prev}\left( {i,k^{\prime}} \right)}} \end{matrix}}{V_{total}(i)}}{R(i)}{\forall{k^{\prime} \in \left\lbrack {{k + 1},K} \right\rbrack}}}$

In one embodiment, the temperature T_(eau)(i,k′+1) is iteratively calculated from T_(eau)(i,k′).

The method according to a first aspect of the invention also comprises, a step 1E4 of determining a preferential minimum power set point P_(c) ^(min_pref)(i,k) as a function of the minimum power set point P_(c) ^(min)(i,k) at the instant k and of the minimum power set point P_(c) ^(min)(i,k+1:K) at the instants k+1 to K.

In one embodiment, the preferential minimum power set point P_(c) ^(min_pref)(i,k) is given by the following formula:

P _(c) ^(min_pref)(i,k)=max(P _(c) ^(min)(i,k),P _(c) ^(min)(i,k+1:K))

At the end of the method 100 according to a first aspect of the invention, it is possible to obtain, for a given consumer i, a preferential minimum power set point P_(c) ^(min_pref)(i,k) for meeting the needs of said consumer regarding hot water. It is subsequently possible to use this information to optimise the management of a plurality of water heaters in view of the electric energy resources.

For this, a second aspect of the invention illustrated in FIG. 2 relates to a method 200 for driving a plurality of water heaters on a network including a plurality of consumers i, each consumer i from the plurality of consumers i comprising a water heater from the plurality of water heaters. The method aims at driving water heaters so as to optimise electric energy consumption, for example to take account of the presence of an intermittent electric energy source such as photovoltaic panels or a wind turbine. More particularly, the method aims at determining, for each consumer i, an optimum power set point at the instant k noted P_(c)(i,k).

The method 200 according to a second aspect of the invention comprises a step 2E1 of receiving, from each consumer i of the plurality of consumers i, a preferential minimum power set point P_(c) ^(min_pref)(i,k). Other data can possibly be received during this step, for example data regarding the state of each consumer i.

For that purpose, in one embodiment, the method according to a second aspect of the invention comprises, before the receiving step 2E1, for each consumer i from the plurality of consumers i, a step 2E0 of implementing a method 100 according to a first aspect of the invention, so as to obtain, for each consumer i, a preferential minimum power set point P_(c) ^(min_pref)(i,k). Once the method 100 according to the first aspect of the invention is implemented, the consumers can send the preferential minimum power set points to a driving system, these being then received during the receiving step 2E1. Other data can possibly be transmitted to the driving system during this step, for example data regarding the state of each consumer i. Such a communication can use for example PLC (Powerline communications) or wireless communication means. These preferential minimum power set points P_(c) ^(min_pref)(i,k) can subsequently be used to determine optimised set points (for example for promoting the use of locally produced electric energy) to each consumer i.

For this, the method according to a second aspect of the invention comprises, for each consumer i from the plurality of consumers i, a step 2E2 of determining a power set point P_(c)(i,k) at the instant k as a function of the preferential minimum power set point P_(c) ^(min_pref)(i,k).

In one embodiment, the step 2E2 of determining a power set point P_(c)(i,k) at the instant k comprises a sub-step 2E21 of determining the optimum electric modulation at the instant k. For example, the optimum electric modulation is the modulation enabling the self-consumption or network service to be maximised. More generally, the optimum electric modulation is a function of the objectives set to the driving method. Determining an optimum electric modulation is known from those skilled in the art and will therefore not be detailed here. The interested reader may for example refer to the problem known as the “Knapsac problem”, and in particular to the document “A dynamic programming method with lists for the knapsac sharing problem”, V. Boyer, D. El Baz, M. Elkihel, Computers & Industrial Engineering, Volume 61, Issue 2, Pages 274-278, 2011. The difficulty therefore does not lie in determining this electric modulation, but in distributing this modulation. In the following, the optimum electric modulation at the instant k will be noted Mod(k).

In one embodiment, the step 2E2 of determining a power set point P_(c)(i,k) at the instant k comprises a sub-step 2E22 of determining an optimum power set point P_(c) ^(opt)(i,k) corresponding to the modulation distribution among each consumer i, said distribution being performed in proportion to the preferential minimum set points. In other words, the optimum power set point P_(c) ^(opt)(i,k) is given by the following formula:

${P_{c}^{opt}\left( {i,k} \right)} = {{{Mod}(k)}\frac{P_{c}^{\min \_ {pref}}\left( {i,k} \right)}{\sum_{i = 1}^{1}{P_{c}^{\min \_ {pref}}\left( {i,k} \right)}}}$

In some cases, it may be advantageous not to distribute the modulation Mod(k) in proportion to the preferential minimum set points, but rather so as to take account of the satisfaction of each consumer i at the instant k, noted S(i,k), said satisfaction S(i,k) being for example equal to 1 when the satisfaction is maximum and to 0 when the latter is minimum. In order to know this satisfaction, it is possible to enable each person associated with a consumer to assess his/her satisfaction. Alternatively, the satisfaction S(i,k) is a function of the amount of hot water and/or the number of persons and/or the hot water temperature in the tank. In one embodiment, the satisfaction S(i,k) is determined using the following formula:

S(i,k)=(T(i,k)−T _(opt)(i,k))²×Per(i,k)

where T_(opt)(i,k) is an optimum temperature of the hot water associated with the consumer i at the instant k. The latter can be chosen for example by the person(s) associated with said consumer i. Alternatively, the latter can be chosen as being equal to a predefined value, for example 55° C.

The distribution is subsequently obtained by determining, for each consumer i, the optimum power P_(c) ^(opt)(i,k) maximising the service satisfaction and the power distribution efficiency, that is maximising the following relationship:

ΣS(i,k)×n(i,k)

where n(i,k) the efficacy of power use is determined using the following formula:

${n\left( {i,k} \right)} = \left\{ \begin{matrix} {{\frac{P_{c}^{opt}\left( {i,k} \right)}{P\left( {i,k} \right)}{si}\mspace{14mu} {P\left( {i,k} \right)}} > 0} \\ {{0\mspace{14mu} {si}\mspace{14mu} {P\left( {i,k} \right)}} = 0} \end{matrix} \right.$

Of course, the maximisation is performed by ensuring that the inequality P(i,k)≥P_(c) ^(min_pref)(i,k) is fulfilled for each consumer i. At the end of this maximisation, each consumer i is associated with an optimum power set point P_(c) ^(opt)(i,k) at the instant k for optimising the latter's satisfaction.

In one embodiment, the step 2E2 of determining a power set point P_(c)(i,k) at the instant k comprises a sub-step 2E23 of determining the power set point P_(c)(i,k), said power set point P_(c)(i,k) at the instant k being the maximum among the optimum power set point P_(c) ^(opt)(i,k) (which corresponds to the modulation distributed between the different consumers i) and the preferential minimum set point P_(c) ^(min_pref)(i,k). It is thus ensured that the preferential minimum set point is always fulfilled.

A third aspect of the invention relates to a device comprising means for implementing a method 100 according to a first aspect of the invention. In one embodiment, the device comprises means for measuring the electric consumption P(i,k) of a water heater as well as the water temperature T(i,k) of said water heater. The device further includes a calculating means (for example a processor) associated with a memory (for example a RAM memory), said memory being configured to store instructions as well as data necessary for carrying out a method 100 according to a first aspect of the invention. In one embodiment, the device also includes communication means (for example means enabling a PLC communication to be established) so that the said device can exchange data with a remote management system.

A fourth aspect of the invention relates to a driving system comprising means for implementing a method 200 according to a second aspect of the invention. In one embodiment, the device includes a calculating means (for example a processor) associated with a memory (for example a RAM memory), said memory being configured to store instructions as well as the data necessary for carrying out a method 200 according to a second aspect of the invention. In one embodiment, the device also includes communication means (for example means enabling a PLC communication to be established) so that said system can exchange data with one or more remote devices, each remote device corresponding to a consumer. 

1. A method for determining a preferential minimum power set point by a consumer i, said consumer comprising an electric water heater, said method comprising: a step of determining the state of the consumer i at an instant k; a step of determining a minimum power set point P_(c) ^(min)(i,k) at the instant k as a function of the state of the consumer i determined during the step of determining the state of the consumer i at an instant k; a step of determining a minimum power set point P_(c) ^(min)(i,k+1:K) at the instants k+1 to K, K being the total number of time ranges during a production/consumption period, as a function of the predicted state of the consumer i estimated from the state of the consumer i determined during step of determining the state of the consumer i at an instant k; a step of determining a preferential minimum power set point P_(c) ^(min_pref)(i,k) as a function of the minimum power set point P_(c) ^(min)(i,k) at the instant k and of the minimum power set point P_(c) ^(min)(i,k+1:K) at the instants k+1 to K.
 2. The method according to claim 1, wherein the step of determining the state of the consumer i at the instant k comprises: a sub-step of acquiring the power P(i,k) consumed by the water heater of the consumer i at the instant k; a sub-step of determining the number of persons Per(i,k) at the instant k associated with said consumer i.
 3. The method according to claim 2, wherein the step of determining the minimum power set point P_(c) ^(min)(i,k) at the instant k comprises: a sub-step of determining the minimum necessary amount of hot water Eau_(min)(i,1:k) at the instant k as a function of the number of persons Per(i,k) associated with the consumer i; a sub-step of determining a minimum power set point P_(c) ^(min)(i,k) at the instant k as a function of the necessary amount of hot water Eau_(min)(i,1:k) at the instant k determined in the previous sub-step.
 4. The method according to claim 3, wherein the step of determining the minimum power set point P_(c) ^(min)(i,k+1:K) at the instants k+1 to K comprises: a sub-step of determining a predicted amount of hot water Eau^(prev)(i,k+1:K) consumed at the instants k+1 to K as a function of a number of persons associated with said consumer i Per⁺¹(i,k+1,K) in which Per⁺¹(i,k)=min(Per(i,k)+1,N_(i)) with N_(i) being the maximum number of persons associated with said consumer i; a sub-step of determining the minimum power set point P_(c) ^(min)(i,k+1:K) at the instants k+1 to K as a function of the predicted amount of hot water Eau^(prev)(i,k+1:K) determined during the previous sub-step.
 5. A method for driving a plurality of water heaters on a network including a plurality of consumers i, each consumer i from the plurality of consumers i comprising a water heater from the plurality of water heaters, said method comprising: for each consumer i from the plurality of consumers i, a step of implementing a method according to one of claims 1 to 4 so as to obtain, for each consumer i, a preferential minimum power set point P_(c) ^(min_pref)(i,k); a step of receiving, for each consumer i from the plurality of consumers i, a preferential minimum power set point P_(c) ^(min_pref)(i,k); for each consumer i from the plurality of consumers i, a step of determining a power set point P_(c)(i,k) at the instant k as a function of the preferential minimum power set point P_(c) ^(min_pref)(i,k).
 6. The method according to claim 5, wherein the step of determining a power set point P_(c)(i,k) at the instant k comprises: a sub-step of determining the optimum electric modulation at the instant k; a sub-step of determining an optimum power set point P_(c) ^(opt)(i,k) corresponding to the modulation distribution among each consumer i, said distribution being performed in proportion to the preferential minimum set points P_(c) ^(min_pref)(i,k); a sub-step of determining the power set point P_(c)(i,k), said power set point P_(c)(i,k) at the instant k being equal to the maximum among the optimum power set point P_(c) ^(opt)(i,k) and the preferential minimum set point P_(c) ^(min_pref)(i,k).
 7. The method according to claim 4, wherein the step of determining a power set point P_(c)(i,k) at the instant k comprises: a sub-step of determining the optimum electric modulation at the instant k; a sub-step of determining an optimum power set point P_(c) ^(opt)(i,k) corresponding to the maximisation of the following relationship: ΣS(i,k)×n(i,k) where S(i,k) is the satisfaction of consumer i at the instant k with S=1 when the satisfaction is maximum and S=0 when the satisfaction is minimum and n(i,k) the efficacy of power use determined using the following formula: ${n\left( {i,k} \right)} = \left\{ \begin{matrix} {{\frac{P_{c}^{opt}\left( {i,k} \right)}{P\left( {i,k} \right)}{si}\mspace{14mu} {P\left( {i,k} \right)}} > 0} \\ {{0\mspace{14mu} {si}\mspace{14mu} {P\left( {i,k} \right)}} = 0} \end{matrix} \right.$ a sub-step of determining the power set point P_(c)(i,k), said power set point P_(c)(i,k) at the instant k being equal to the maximum among the optimum power set point P_(c)(i,k) and the preferential minimum set point P_(c) ^(min_pref)(i,k).
 8. A device comprising means for implementing a method according to claim
 1. 9. A computer program comprising instructions which cause the device according to the previous claim 1 to carry out the steps of the method.
 10. A non-transitory computer readable medium, comprising instructions to carry out the steps of the method according to claim
 1. 